Solve the following problems by using the inverse of the matrix involved.

(a) An automobile factory produces twomodels, A and B. Model A requires 1 labor hour to paint and

1/2 labor hour topolish; model B requires 1 labor hour for each process. During each hour that the assembly line isoperating, there are 100 labor hours available for painting and 80 labor hours for polishing. How many of each model can be produced each hour if all the labor hours available are to beutilized?

(b) Suppose each model A requires 10 widgets and 14 shims and each model B requires 7 widgets and 10 shims. The factory can obtain 760 widgets and 1070 shims each hour. How many cars of each model can it produce while using all the partsavailable?

(a) ModelA:

(a) ModelB:

(b) ModelA:

(b) ModelB: